Michael Brandenbursky

activity

20092026

most citedCancelation norm and the geometry of biinvariant word metrics

17 citations · 71 across the 20 of their papers we have counts for

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26 papers · 1 filter

math.GT2026

Bounded cohomology of transformation groups in all degrees

Michael Brandenbursky

Let $M$ be a compact connected oriented smooth manifold, of dimension $n \geq 2$ . Let $T_{M} G$ be one of the following transformation groups: $H o m e o_{0} (M, μ)$ , $D i f f_{0} (M, μ)$ , $Sy…

math.GT2025

On quasimorphisms and distortion in homeomorphism groups

Michael Brandenbursky, Jarek Kedra, Michal Marcinkowski +1

Let $M$ be a smooth compact oriented connected manifold, and $Homeo_{0} (M, μ)$ the group of homeomorphisms of $M$ supported away from $\partial M,$ which preserve a Borel probab…

math.GT2025

The $L^{p}$ -diameter of the space of contractible loops

Michael Brandenbursky, Egor Shelukhin

We prove that the space of contractible simple loops of a given fixed area in any compact oriented surface has infinite diameter as a homogeneous space of the group of area-preserv…

math.GT2025

Bounded cohomology of measure-preserving homeomorphism groups of non-orientable surfaces

Michael Brandenbursky, Lior Menashe

Let $N_{g}$ be a closed non-orientable surface of genus $g \geq 3$ , and let $Homeo_{0} (N_{g}, μ)$ be the identity component of its group of measure-preserving homeomorphisms.…

math.GT2023

Volume and Euler classes in bounded cohomology of transformation groups

Michael Brandenbursky, Michał Marcinkowski

Let $M$ be an oriented smooth manifold, and $Homeo (M, ω)$ the group of measure preserving homeomorphisms of $M$ , where $ω$ is a finite measure induced by a volume for…

math.GT2021

The Schwarz-Milnor lemma for braids and area-preserving diffeomorphisms

Michael Brandenbursky, Michał Marcinkowski, Egor Shelukhin

We prove a number of new results on the large-scale geometry of the $L^{p}$ -metrics on the group of area-preserving diffeomorphisms of each orientable surface. Our proofs use in a ke…

math.GT2019

On the entropy norm on $H am (S^{2})$

Michael Brandenbursky, Egor Shelukhin

In this note we prove that for each positive integer $m$ there exists a bi-Lipschitz embedding $Z^{m} \to H am (S^{2})$ , where $H am (S^{2})$ is equipped with the entropy metric. In particula…

math.GT2019

Bounded cohomology of transformation groups

Michael Brandenbursky, Michal Marcinkowski

Let $M$ be a complete connected Riemannian manifold of finite volume. In this paper we present a new method of constructing classes in bounded cohomology of transformation groups s…

math.GT2018

Fragmentation norm and relative quasimorphisms

Michael Brandenbursky, Jarek Kędra

We prove that manifolds with complicated enough fundamental group admit measure-preserving homeomorphisms which have positive stable fragmentation norm with respect to balls of bou…

math.GT2018

On the entropy norm on the group of diffeomorphisms of closed oriented surface

Michael Brandenbursky, Arpan Kabiraj

We prove that the entropy norm on the group of diffeomorphisms of a closed orientable surface of positive genus is unbounded.

math.GT2017

Entropy and quasimorphisms

Michael Brandenbursky, Michał Marcinkowski

Let $S$ be a compact oriented surface. We construct homogeneous quasimorphisms on $D i f f (S, a r e a)$ , on $D i f f_{0} (S, a r e a)$ and on $H am (S)$ generalizing the constructions of Gambaudo-G…

math.GT2017

Aut-invariant norms and Aut-invariant quasimorphisms on free and surface groups

Michael Brandenbursky, Michał Marcinkowski

Let $F_{n}$ be the free group on $n$ generators and $Γ_{g}$ the surface group of genus $g$ . We consider two particular generating sets: the set of all primitive elements in $F_{n}$ and t…

math.GT2016

Concordance of certain 3-braids and Gauss diagrams

Michael Brandenbursky

Let $β := σ_{1} σ_{2}^{- 1}$ be a braid in $B_{3}$ , where $B_{3}$ is the braid group on 3 strings and $σ_{1}, σ_{2}$ are the standard Artin generators. We use Gauss diagram formulas to show that f…

math.GT2016★ 6 cited

The $L^{p}$ -diameter of the group of area-preserving diffeomorphisms of $S^{2}$

Michael Brandenbursky, Egor Shelukhin

We show that for each $p \geq 1,$ the $L^{p}$ -metric on the group of area-preserving diffeomorphisms of the two-sphere has infinite diameter. This solves the last open case of a conj…

math.GT2014★ 7 cited

Concordance group and stable commutator length in braid groups

Michael Brandenbursky, Jarek Kędra

We define a quasihomomorphism from braid groups to the concordance group of knots and examine its properties and consequences of its existence. In particular, we provide a relation…

math.GT2013★ 17 cited

Cancelation norm and the geometry of biinvariant word metrics

Michael Brandenbursky, Światosław R. Gal, Jarek Kędra +1

We study biinvariant word metrics on groups. We provide an efficient algorithm for computing the biinvariant word norm on a finitely generated free group and we construct an isomet…

math.GT2013

Bi-invariant metrics and quasi-morphisms on groups of Hamiltonian diffeomorphisms of surfaces

Michael Brandenbursky

Let Σ_g be a closed orientable surface let Diff_0(Σ_g; area) be the identity component of the group of area-preserving diffeomorphisms of Σ_g. In this work we present an extension…

math.GT2013

On the autonomous metric on groups of Hamiltonian diffeomorphisms of closed hyperbolic surfaces

Michael Brandenbursky

Let $Σ_{g}$ be a closed hyperbolic surface of genus $g$ and let $H am (Σ_{g})$ be the group of Hamiltonian diffeomorphisms of $Σ_{g}$ . The most natural word metric on this group is the aut…

math.GT2013★ 8 cited

On the large-scale geometry of the L^p-metric on the symplectomorphism group of the two-sphere

Michael Brandenbursky, Egor Shelukhin

We prove that the vector space R^d of any finite dimension d with the standard metric embeds in a bi-Lipschitz way into the group of area-preserving diffeomorphisms G of the two-sp…

math.GT2013★ 1 cited

Coloring Link Diagrams And Conway-type Polynomial Of Braids

Michael Brandenbursky

In this paper we define and present a simple combinatorial formula for a 3-variable Laurent polynomial invariant of conjugacy classes in Artin braid group $B_{m}$ . We show that this…

math.GT2012

Invariants of closed braids via counting surfaces

Michael Brandenbursky

A Gauss diagram is a simple, combinatorial way to present a link. It is known that any Vassiliev invariant may be obtained from a Gauss diagram formula that involves counting subdi…

math.GT2012★ 6 cited

Link invariants via counting surfaces

Michael Brandenbursky

A Gauss diagram is a simple, combinatorial way to present a knot. It is known that any Vassiliev invariant may be obtained from a Gauss diagram formula that involves counting (with…

math.GT2012★ 15 cited

On the autonomous metric on the group of area-preserving diffeomorphisms of the 2-disc

Michael Brandenbursky, Jarek Kedra

Let $D^{2}$ be the open unit disc in the Euclidean plane and let $G := D i f f (D 2; a r e a)$ be the group of smooth compactly supported area-preserving diffeomorphisms of $D^{2}$ . We investig…

math.GT2011★ 8 cited

Quasi-morphisms and L^p-metrics on groups of volume-preserving diffeomorphisms

Michael Brandenbursky

Let M be a smooth compact connected oriented manifold of dimension at least two endowed with a volume form. We show that every homogeneous quasi-morphism on the identity component…

Bounded cohomology of transformation groups in all degrees

On quasimorphisms and distortion in homeomorphism groups

The Lp-diameter of the space of contractible loops

Bounded cohomology of measure-preserving homeomorphism groups of non-orientable surfaces

Volume and Euler classes in bounded cohomology of transformation groups

The Schwarz-Milnor lemma for braids and area-preserving diffeomorphisms

On the entropy norm on Ham(S2)

Bounded cohomology of transformation groups

Fragmentation norm and relative quasimorphisms

On the entropy norm on the group of diffeomorphisms of closed oriented surface

Entropy and quasimorphisms

Aut-invariant norms and Aut-invariant quasimorphisms on free and surface groups

Concordance of certain 3-braids and Gauss diagrams

The Lp-diameter of the group of area-preserving diffeomorphisms of S2

Concordance group and stable commutator length in braid groups

Cancelation norm and the geometry of biinvariant word metrics

Bi-invariant metrics and quasi-morphisms on groups of Hamiltonian diffeomorphisms of surfaces

On the autonomous metric on groups of Hamiltonian diffeomorphisms of closed hyperbolic surfaces

On the large-scale geometry of the L^p-metric on the symplectomorphism group of the two-sphere

Coloring Link Diagrams And Conway-type Polynomial Of Braids

Invariants of closed braids via counting surfaces

Link invariants via counting surfaces

On the autonomous metric on the group of area-preserving diffeomorphisms of the 2-disc

Quasi-morphisms and L^p-metrics on groups of volume-preserving diffeomorphisms

The $L^{p}$ -diameter of the space of contractible loops

On the entropy norm on $H am (S^{2})$

The $L^{p}$ -diameter of the group of area-preserving diffeomorphisms of $S^{2}$